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Robust direction estimation. (English) Zbl 0761.62035

The study of the stability of parameter estimates for directional data dates back to the late sixties and this paper is an interesting contribution to this domain. The authors consider rotationally symmetric models for directional data with axis of rotation \(\mu\) and concentration parameter \(\kappa\). The prototype is the von Mises distribution. The aim of the authors is focused primarily on the stability of estimates of \(\mu\), but they show that the results can be easily adapted to the more general class of models. Another part is devoted to the notion of standardized bias robustness for direction estimates, where the standardizing with respect to the Kullback-Leibler distance is suggested. The authors obtained a sharp upper bound on the breakdown point of any estimator that is Fisher consistent for rotationally symmetric distributions and gave a sufficient condition for a direction estimate to achieve the bound on the breakdown point. Finally, they focused on the circular case and studied, e.g., the robustness of the circular median.
Reviewer: J.Antoch (Praha)

MSC:

62F35 Robustness and adaptive procedures (parametric inference)
62F12 Asymptotic properties of parametric estimators
62H12 Estimation in multivariate analysis
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